That's one of the first things I did, actually. After dumping the contents of the flash off, I went on Amazon and hit 'reorder' on the same SD card that I'd bought before. Unfortunately, it was not the same: in the picture [1], the left is the one I'd purchased this time, and the right is the one I'd destroyed. The deals that low-cost SD card makers get on NAND flash vary greatly from day to day, so they just manufacture based on whatever controller and flash combination they can get cheapest on any given day: even the same SKU is unlikely to stay the same internally very long.
I did also try soldering to the BGA pads on the damaged one [2] [3], but no joy: I imagine that there were some traces that went backwards on the board before going towards the controller (for instance, to meet the TSOP leads), and on inserting the SD card into my laptop, I still had no signs of life.
[1] http://joshuawise.com/photos/etc/sd-card/sd-fux-11.xscale.jp...
[2] http://joshuawise.com/photos/etc/sd-card/sd-fux-13.xscale.jp...
[3] http://joshuawise.com/photos/etc/sd-card/sd-fux-15.xscale.jp...